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Ill-posed inverse problems and their optimal regularization

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  • Läuter, Henning
  • Liero, H.

Abstract

The regularization of ill-posed systems of equations is carried out by corrections of the data or the operator. It is shown how the efficiency of regularizations can be calculated by statistical decision principles. The efficiency of nonlinear regularizations depends on the distribution of the admitted disturbances of the data. For the class of linear regularizations optimal corrections are given.

Suggested Citation

  • Läuter, Henning & Liero, H., 1997. "Ill-posed inverse problems and their optimal regularization," SFB 373 Discussion Papers 1997,57, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199757
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    References listed on IDEAS

    as
    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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